Abstract
For quite some time, the geometry-dependence of electric fields confined in two-dimensional systems of propagation has been known. We explore a lesser known way in which one can confine light, parabolically. One can use this method to understand the different forms modes take in such fibers and the appropriate eigenfunction for spectral analysis. In this paper, a fiber with a parabolic core and a circular cladding for the preservation of coaxiality are proposed.
Funding statement: This article was supported by Division of Electrical, Communications and Cyber Systems, Funder Id: http://dx.doi.org/10.13039/100000148, Grant Number: GA11075.
Acknowledgements
We would like to thank University of Virginia Professor of Mathematics Zoran Grujić for his help in supervising and editing this manuscript through the drafts and subsequent revisions and overseeing meticulous derivation of the equations. His specialization in partial differential equations applied in curvilinear coordinates was especially helpful for this paper.
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